On the moduli of continuity and fractional-order derivatives in the problems of best mean-square approximation by entire functions of the exponential type on the entire real axis

DOI10.1007/s11253-017-1389-4zbMath1499.41038OpenAlexW2736296330WikidataQ115602771 ScholiaQ115602771MaRDI QIDQ1729626

Xianqiang Yang

Publication date: 27 February 2019

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-017-1389-4

zbMATH Keywords

exact Jackson-type inequalitiesmodules of continuity of fractional order

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by other special function classes (41A30) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (2)

Generalized characteristics of smoothness and some extreme problems of the approximation theory of functions in the space \(L_2(\mathbb{R})\). II ⋮ Generalized characteristics of smoothness and some extreme problems of the approximation theory of functions in the space \(L_2(\mathbb{R})\). I

Cites Work

• On some extremal problems of approximation theory of functions on the real axis. II
• Classes of functions defined on the real axis and their approximations by entire functions. II
• Best mean-square approximation of functions defined on the real axis by entire functions of exponential type
• On some extremal problems of approximation theory of functions on the real axis. I
• Jackson-type inequalities for the special moduli of continuity on the entire real axis and the exact values of mean \(\nu\)-widths for the classes of functions in the space \(L_2(\mathbb R)\)
• On the best mean square approximations by entire functions of exponential type in \(L_2(\mathbb R)\) and mean \(\nu\)-widths of some functional classes
• Best mean-square approximations by entire functions of exponential type and mean \(\nu\)-widths of classes of functions on the line
• Classes of functions defined on the real line and their approximation by entire functions. I
• Exact constants in Jackson-type inequalities for L 2-approximation on an axis
• Best Trigonometric Approximation, Fractional Order Derivatives and Lipschitz Classes
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